제출 #473733

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
473733		jalsol	Harbingers (CEOI09_harbingers)	C++17	50 / 100	137 ms	17988 KiB

harbingers

// looking to shine brighter in this world...

#define TASK "harbingers"

#ifdef LOCAL
#include "local.h"
#else
#include <bits/stdc++.h>
#define debug(...)
#define DB(...)
#endif

using namespace std;

using ll = long long;
using ld = long double;

#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define fi first
#define se second

#define For(i, l, r) for (int i = (l); i <= (r); ++i)
#define Ford(i, r, l) for (int i = (r); i >= (l); --i)
#define Rep(i, n) For (i, 0, (n) - 1)
#define Repd(i, n) Ford (i, (n) - 1, 0)
#define Fe(...) for (auto __VA_ARGS__)

template <class C> inline int isz(const C& c) { return static_cast<int>(c.size()); }
template <class T> inline bool chmin(T& a, const T& b) { return (a > b) ? a = b, true : false; }
template <class T> inline bool chmax(T& a, const T& b) { return (a < b) ? a = b, true : false; }

const bool __initialization = []() {
    cin.tie(nullptr)->sync_with_stdio(false);
    if (fopen(TASK".inp", "r")) {
        (void)(!freopen(TASK".inp", "r", stdin));
        (void)(!freopen(TASK".out", "w", stdout)); }
    cout << setprecision(12) << fixed;
    return true;
}();

constexpr ld eps = 1e-9;
constexpr int inf = 1e9;
constexpr ll linf = 1e18;

// =============================================================================

constexpr int maxn = 1e5 + 5;

struct Data {
    int v; ll c;

    Data() : v(0), c(0) {}
    Data(int _v, ll _c) : v(_v), c(_c) {}
};

struct Town {
    ll init, speed;

    Town() : init(0), speed(0) {}
    Town(ll _i, ll _s) : init(_i), speed(_s) {}
};

struct Line {
	mutable ll k, m, p;
	bool operator<(const Line& o) const { return k < o.k; }
	bool operator<(ll x) const { return p < x; }
};

struct LineContainer : multiset<Line, less<>> {
	// (for doubles, use inf = 1/.0, div(a,b) = a/b)
	static const ll inf = LLONG_MAX;
	ll div(ll a, ll b) { // floored division
		return a / b - ((a ^ b) < 0 && a % b); }
	bool isect(iterator x, iterator y) {
		if (y == end()) return x->p = inf, 0;
		if (x->k == y->k) x->p = x->m > y->m ? inf : -inf;
		else x->p = div(y->m - x->m, x->k - y->k);
		return x->p >= y->p;
	}
	void add(ll k, ll m) {
		auto z = insert({k, m, 0}), y = z++, x = y;
		while (isect(y, z)) z = erase(z);
		if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
		while ((y = x) != begin() && (--x)->p >= y->p)
			isect(x, erase(y));
	}
	ll query(ll x) {
		assert(!empty());
		auto l = *lower_bound(x);
		return l.k * x + l.m;
	}
};

int n;
vector<Data> g[maxn];
Town a[maxn];

LineContainer hull;
ll dp[maxn];
ll dist[maxn];

void Dfs(int u, int p) {
    dp[u] = a[u].init + a[u].speed * dist[u]
            - hull.query(a[u].speed);

    hull.add(dist[u], -dp[u]);

    Fe (&[v, c] : g[u]) {
        if (v == p) continue;
        dist[v] = dist[u] + c;
        Dfs(v, u);
    }
}

signed main() {
    cin >> n;

    Rep (_, n - 1) {
        int u, v; ll c; cin >> u >> v >> c;
        g[u].emplace_back(v, c);
        g[v].emplace_back(u, c);
    }

    For (i, 2, n) cin >> a[i].init >> a[i].speed;

    hull.add(0, 0);
    Dfs(1, -1);

    // dp[u] + a[v].init + a[v].speed * (dist[v] - dist[u])
    // dp[u] + s[v] + v[v] * (d[v] - d[u])
    // dp[u] + s[v] + v[v] * d[v] - v[v] * d[u]
    // s[v] + v[v] * d[v] - v[v] * d[u] + dp[u]
    // s[v] + v[v] * d[v] + f(v[v])

    For (i, 2, n) {
        cout << dp[i] << " \n"[i == n];
    }

    return 0;
}

• Subtask 1: 50 / 100